The Analysis of Vacuum Cleaner Weights: Is There a Significant Difference?
The Table of Vacuum Cleaner Weights
The table available below shows the weights (in pounds) for a sample of vacuum cleaners. The weights are classified according to vacuum cleaner type.
| Bagged Upright | Bagless Upright | Top Canister |
|---|---|---|
| 22 | 21 | 24 |
| 21 | 18 | 23 |
| 24 | 24 | 25 |
| 23 | 22 | 27 |
| 19 | 18 | 26 |
| 25 | 22 | 27 |
Looking for Test Statistic
At a = 0.05, can you conclude that at least one mean vacuum cleaner weight is different from the others?
Question:
Based on the given data, can we conclude that at least one mean vacuum cleaner weight is different from the others at a significance level of 0.05?
Answer:
Final answer: Yes, we can conclude that at least one mean vacuum cleaner weight is different from the others at a significance level of 0.05.
Explanation: To determine if at least one mean vacuum cleaner weight is different from the others, we can use a one-way analysis of variance (ANOVA) test. The ANOVA test compares the means of multiple groups to determine if there is a statistically significant difference between them.
In this case, we have three types of vacuum cleaners: Bagged upright, Bagless upright, and Top canister. We have weights for each type of vacuum cleaner as shown in the table.
We can calculate the test statistic, which is the F-statistic, using the formula: F = (Between-group variability) / (Within-group variability). The between-group variability measures the differences between the means of the groups, while the within-group variability measures the differences within each group.
Once we have calculated the test statistic, we can compare it to the critical value from the F-distribution table at a significance level of 0.05. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that at least one mean vacuum cleaner weight is different from the others.